Dividing f(x) by zero.

Question

I'm currently studying calculus, and have learned some useful facts regarding operations that can be carried out on a function. For example:

y = f(x) + z

If we plot f(x), then plot the above, the line will be moved up on the y axis by z for every z > 0, or will be moved down by z for every z < 0 relatively to f(x) line.

Similarly if I would multiply f(x) by z, the line would be moved up or down by z amount relatively to f(x) line depending if z is a negative or positive value.

But is it true to state that the following cannot be defined / ploted?

y = f(x) / 0

You cannot plot the above (I presume).

Answer 1

You cannot plot $y = f(x)/0$ since it's not even defined.

Answer 2

You are correct; $f(x)/0$ cannot be plotted. Consider the special case where $x=1$. So then we have $f(1)$; what is this? This is just a number. But we can't divide a number by $0$; that value is undefined. So we can't plot it. And since this is true for all $x$, the entire function $f(x)/0$ isn't defined anywhere and can't be plotted anywhere.

Answer 3

It is correct that you cannot plot $y=\frac{f(x)}{0}$, since it is not defined at $0$. Or anywhere else. Thanks Saulspatz.